Acoustic VTI Full-waveform Inversion with 3-D Free-surface Topography

Abstract

In land applications, topography variation may impact the imaging if not taken into account. With low-frequency and wide-aperture data, the long-to-intermediate wavelength components of the velocity model can be recovered by full-waveform inversion. Standard static corrections to handle the topography do not work satisfactorily on long-offset data. We present a method to handle 3-D free-surface topography for acoustic FWI by directly modelling the effect of the topography with a finite-difference scheme for the first-order wave equation introduced earlier (Huiskes et al., 2016; Mulder and Huiskes, 2017). The method is based on an immersed interface approach (Lombard et al., 2008) in which the free surface does not have to coincide with the discretization grid, avoiding a staircase-like representation of the topography (Bohlen and Saenger, 2006). We refer to Huiskes et al. (2016) for a more detailed overview of methods for simulating seismic waves interacting with free-surface topography. First, we review the main elements of the numerical scheme that is designed specifically for discretization on standard staggered grids (SSG) using high-order derivative operators, which are modified based on their relative position to the free surface. Next, we extend the approach to vertical transverse isotropic (VTI) media to be able to model velocity anisotropy required in long-offset inversions. In relatively simple synthetic experiments, we then reproduce topography artefacts we have seen on real land fullwaveform inversions, allowing us to quantify the effect of elevation variation on the inversion accuracy.